Origin Stories:
Emerald Dawn #1-6, Emerald Dawn II #1-6, and Secret Origin storyarc:

Early Appearances of Sinestro:
Green Lantern/Green Arrow #91, GL v2 #124-125, GL v2 #150, GL Corps v1 #217, GL Corps v1 #222:

Green Lantern v3 Key Issues:
GL v3 #1-1st issue, GL v3 #25-Guy Gardner loses GL ring and quits Corps, GL v3 #46-The Cyborg Superman destroys Coast City (Hal's hometown), GL v3 #48-50-Emerald Twilight story death of GL Corps 1st Parallax and 1st Kyle Rayner, GL v3 #51-1st Kyle Rayner issue, GL v3 #81-Hal Jordan's Funeral, GL v3 #100-106-Emerald Knights story Hal Jordan returns temporarily, GL v3 #108-Jade becomes a GL, GL v3 #146-1st Appearance of Ion, GL v3 #151-1st Appearance of New Costume, GL v3 #154-Controversial Gay Bashing Issue, GL v3 #181-Final Kyle Rayner Issue


Green Lantern Corps Key Issues:
Tales of the GL Corps #1-3, Tales of the GL Corps Annual #1-3, GL Corps v1 #201-1st issue previously was GL v2, GL Corps #224-Final issue and Power Battery is destroyed, GL Corps Quarterly #1-1st Issue, GL Corps Recharge #1-5-GL Corps Returns, GL Corps v2 #1-1st Issue of Modern Series:


Important John Stewart issues:
GL v2 #181-First appearance of John Stewart as the main Green Lantern, GL V2 #188-John reveals identity to world, Cosmic Odyssey #1-3-John destroys an entire world (#1 signed by Mike Mignolia), Darkstars #1-John becomes a Darkstar, GL v3 #74-John's legs are paralyzed, GL v3 #150-John regains leg use and becomes GL again, Action Comics #601-Katma Tui (John's wife) is killed by Star Sapphire:


Important Guy Gardner Issues:
GL v2 #195-Guy Gardner becomes a regular GL (Signed by Steve Englehart), Justice League #1-Guy becomes a member of the JLA, GL v3 #25-Guy loses his GL Ring, Guy Gardner: Reborn #1-3-Guy Gardner gains Yellow Ring, Guy Gardner #1-1st solo comic, Guy Gardner: Warrior #17-First retitled issue, Guy Gardner: Warrior #17-21-Emerald Fallout story Parallax destroys Guy's Yellow Ring, Guy Gardner: Warrior #0-1st apperance of Guy's Vuldarian powers, Justice League America #100-Guy rejoins JLA as Warrior, GL: Emerald Warriors #1-1st issue of modern series:

Ion:

Infinity Inc. v1 #25-1st Apperance of Jade (and the rest of Infinity Inc.):

Alternate Universe Green Lanterns:
Green Lantern Annual #3-Elseworlds, Green Lantern Annual #4-Legends of the Dead Earth, Green Lantern: Tangent #1, Green Lantern: Dragon Lord #1-3, Green Lantern: 1001 Emerald Nights, Iron Lantern #1:

Trinity:

Green Lantern/Sentinel: Heart of Darkness:

Green Lantern: Rebirth #1-6 and Green Lantern v4 #1:

Mystery of the Star Sapphire:

The Sinestro Corps War:

Rage of the Red Lanterns:

Agent Orange:

The Blackest Night:


The War of the Green Lanterns:

DC New 52 #1 Issues:

Green Lantern: Secret Files and Origins:

Random GL Issues:
Green Lantern Special #1 and 2, Green Lantern: Mosaic #1, Green Lantern: Ganthet's Tale, Green Lantern: Fear Itself, Green Lantern/Silver Surfer, Parallax #1, Green Lantern Gallery, The Last Will and Testament of Hal Jordan, Green Lantern: Circle of Fire #1-2, Green Lantern: The New Corps #1-2, Green Lantern Versus Aliens #1-4:


Green Lantern Wizard Magazine Covers:

Green Lantern Novels:

Green Lantern Trading Cards:






Green Lantern Action Figures:



Green Lantern Movies:

Green Lantern Power Rings Collectibles:

Green Lantern Pins:

Random Green Lantern Collectibles:



Green Lantern Poster:

I also have the entire run of the current Green Lantern series, every single issue, every single one-shot, and every single mini-series attached to it as well. But that would be hard to get into a picture.